a) Power:
The power output of the turbine can be calculated using the following formula:
Power = (Head × Flow rate × Gravity) / Overall efficiency
Where gravity is the acceleration due to gravity (approximately 9.81 m/s²).
Substituting the given values:
Power = (5 m × 120 m³/s × 9.81 m/s²) / 0.8
Power ≈ 9112.5 kW
b) Specific speed:
Specific speed (Ns) is a dimensionless parameter used to characterize the performance of a turbine. It can be calculated using the following formula:
Ns = (N √Q) / H^(3/4)
Where N is the runner speed in revolutions per minute, Q is the flow rate in cubic meters per second, and H is the head in meters.
Substituting the given values:
Ns = (120 rev/min √120 m³/s) / (5 m)^(3/4)
Ns ≈ 774.12
c) Exit angle of the inlet guide vanes:
The exit angle of the inlet guide vanes can be calculated using the following formula:
Exit angle = Blade angle of entry - Hub tip ratio × 90°
Substituting the given values:
Exit angle = 60° - 0.4 × 90°
Exit angle ≈ 24°
d) Exit angle of runner blades:
The exit angle of the runner blades in an axial flow turbine is approximately equal to the exit angle of the inlet guide vanes. Therefore, the exit angle of the runner blades would also be approximately 24°.
e) Hydraulic efficiency:
Hydraulic efficiency (ηh) can be calculated using the following formula:
ηh = (Head × Flow rate × Gravity × Overall efficiency) / (Power / 1000)
Substituting the given values:
ηh = (5 m × 120 m³/s × 9.81 m/s² × 0.8) / (9112.5 kW / 1000)
ηh ≈ 0.537 or 53.7%
To summarize:
a) Power ≈ 9112.5 kW
b) Specific speed ≈ 774.12
c) Exit angle of the inlet guide vanes ≈ 24°
d) Exit angle of runner blades ≈ 24°
e) Hydraulic efficiency ≈ 53.7%